Our interactions with touchscreens rely heavily on vision: we press virtual buttons and push virtual sliders that provide no mechanical sense of the object they seek to represent. We report here PopTouch: a 500 μm thick flexible haptic display that creates pressable physical buttons on demand. PopTouch can be mounted directly on touchscreens or any other smooth surface, flat or curved. The buttons of PopTouch are independently controlled hydraulically amplified electrostatic zipping taxels (tactile pixels) that generate 1.5 mm of out of plane displacement. When pressed by the user, the buttons provide intuitive mechanical feedback thanks to a snap‐through characteristic in their force‐displacement profile. The snap‐through threshold can be as high as 4 N, and is tuned by design and actuation parameters. We present two versions of PopTouch: a transparent PopTouch for integration on Touchscreens with built‐in touch sensing, such as smartphones and a sensorized PopTouch, with embedded thin‐film piezoelectric sensors on each taxel, for integration on substrates without built‐in touch sensing, such as a steering wheel. PopTouch adds static and vibrating button‐like haptics to any device thanks to its thin profile, flexibility, low power consumption (6 mW per button), rapid refresh rate (2 Hz), and freely configured array format.This article is protected by copyright. All rights reserved